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Simplifying x(x2 + -4x) = 6(x2 + -4x) Reorder the terms: x(-4x + x2) = 6(x2 + -4x) (-4x * x + x2 * x) = 6(x2 + -4x) (-4x2 + x3) = 6(x2 + -4x) Reorder the terms: -4x2 + x3 = 6(-4x + x2) -4x2 + x3 = (-4x * 6 + x2 * 6) -4x2 + x3 = (-24x + 6x2) Solving -4x2 + x3 = -24x + 6x2 Solving for variable 'x'. Reorder the terms: 24x + -4x2 + -6x2 + x3 = -24x + 6x2 + 24x + -6x2 Combine like terms: -4x2 + -6x2 = -10x2 24x + -10x2 + x3 = -24x + 6x2 + 24x + -6x2 Reorder the terms: 24x + -10x2 + x3 = -24x + 24x + 6x2 + -6x2 Combine like terms: -24x + 24x = 0 24x + -10x2 + x3 = 0 + 6x2 + -6x2 24x + -10x2 + x3 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 24x + -10x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(24 + -10x + x2) = 0 Factor a trinomial. x((4 + -1x)(6 + -1x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {0, 4, 6}
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